By the proof of Lemma 2.1 we may consider a framed circle \((S^{1},F)\)  as a
tubular neighborhood of the embedding \(S^{1}\subset M\) ; project on the
factor \(D^{n-1}\) , and shrink the boundary to a point \(\infty \) , giving a
sphere \(S^{n-1}\) , and finally extend the map of the tubular neighborhood to \(M\)  by mapping the complement to \(\infty \) . We have defined a map \(M\rightarrow S^{n-1}\)  whose homotopy class is denoted by \(\gamma _{1}(S^{1},F)\in [M,S^{n-1}]\) . Combining Lemma 2.1 with the
Thom-Pontryagin theorem [1]} one sees that the map
